I was going under the presumption that one would be exchanging same for same, as far as uppers go. Of course, as you've stated, you can't put a pistol upper on a lower that's already been made into a rifle. You can't go from rifle to pistol or SBR configuration without playing (and paying) the NFA game; once it becomes a "rifle," then that's it, you're stuck with that unless you file and pay. However, you can still swap any RIFLE upper (16"+ barrel and 26"+ overall when assembled) onto any RIFLE lower. Doesn't matter if it's your upper or someone else's - again, you can own one AR lower and several uppers of various calibers. Nothing specifies that the upper receiver must belong to you to be used on your lower receiver, as the upper receiver is not serialized and is basically just a "part" that you can order (completely assembled, or piece by piece, or as a you-assemble-it kit) and have sent right to your door with no FFL ... just like a stock, grip, handguard, muzzle brake, sights, etc. You're fine as long as the NFA lower registered to you still remains yours and doesn't change ownership, and you're not changing its classification from rifle to pistol or SBR - again, as you mentioned, I'm not sure if it being a registered full-auto makes a difference or not as far as barrel lengths.
It doesn't matter if that is your one-and-only AR receiver in the world, and you've got a hundred different complete rifle-length AR uppers of various calibers, colors, barrel lengths (over 16"), and whatnot ... or if you just have that one receiver and you've got twenty buddies with different uppers that they want you to slap on there and try out with it. The "firearm" (the lower receiver, the serialized part) still hasn't changed ownership or definition, as long as it's still a rifle (or SBR or handgun, whatever you registered it as being in your NFA paperwork) and as long as it's still legally owned by you.
Long story short, with the above scenario, all the ATF technically cares about is: 1. who owns the serialized part (the "firearm"), 2. barrel length, and 3. overall length. Well, and you obviously can't loan it to anyone that's legally prohibited from owning or having access to firearms, but that's true regardless of whether it's an NFA item or not.